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Graph Structure and Monadic Second-Order Logic by Joost Engelfriet, Bruno Courcelle

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3.4 The recognizable sets of an algebra

In the previous three sections, we have defined and studied the equational sets of an algebra. These sets generalize the context-free languages, and also the regular languages (of words and terms). We now define the recognizable sets, and so generalize the characterization of regular languages formulated in terms of finite congruences.

3.4.1 Definitions and examples

An F-algebra is locally finite if each domain As is finite. It is finite if, furthermore, its set of sorts is finite (although F may be infinite). ...

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